HiHTP: A custom-tailored hierarchical sparse detector for massive MTC

Abstract

Recently, a new class of so-called hierarchical thresholding algorithms was introduced to optimally exploit the sparsity structure in joint user activity and channel detection problems. In this paper, we take a closer look at the user detection performance of such algorithms under noise and relate its performance to the classical block correlation detector with orthogonal signatures. More specifically, we derive a lower bound for the diversity order which, under suitable choice of the signatures, equals that of the block correlation detector. Surprisingly, in specific parameter settings non-orthogonal pilots, i.e. pilots where (cyclically) shifted versions interfere with each other, outperform the block correlation detector. Altogether, we show that, in wide parameter regimes, the hierarchical thresholding detectors behave like the classical correlator with improved detection performance but operate with much less required pilot subcarriers. We provide mathematically rigorous and easy to handle formulas for numerical evaluations and system design. Finally, we evaluate our findings with numerical examples and show that, in a practical parameter setting, a classical pilot channel can accommodate up to three advanced pilot channels with the same performance.

Hierarchical Sparse Recovery from Hierarchically Structured Measurements with Application to Massive Random Access

“…Our work generalizes prior work on compressed sensing of hierarchically sparse signals from Kronecker-structured measurements [7] and directly implies recovery guarantees for these measurement operators for a large class of hierarchically structured thresholding algorithms. In particular, we also numerically show that the fast, low-complexity HiHTP algorithm [10] is able to solve the resulting structured compressed sensing problems reliably under additive Gaussian noise. Moreover, we numerically demonstrate that HiHTP is capable of correctly detecting the non-vanishing blocks (e.g.…”

Detection Techniques for Massive Machine-Type Communications: Challenges and Solutions

“…Lehmann derived in [54] an inference algorithm based on message-passing resulting in an iterative code-aided receiver. The work in [55] compares different approaches of the Hierarchical Hard Thresholding Pursuit (HiHTP) algorithm. Machine learning approaches are also suggested, as in [56]- [60].…”

“…On the other hand, the techniques in [52] and [53] consider the prior distribution of the channel vecto and show better performance, as shown in Figs.16a and 16b referred to as the activity detection performance. Using the method of moments, the Iterative EP [53] has a much better Average SNR (dB) NMSE AMP AMP with MMSE denoiser [46] MP-BSBL [54] BOMP with known K [103] Iterative EP [55] Oracle MMSE NMSE performance compared to the other schemes, while its computational complexity is quadratic and that of MP-BSBL [52] is linear. The well-known BOMP [106] algorithm with knowledge of the the number of active devices is used as a lower bound for MP-BSBL, as done in the original paper.…”

Secure massive IoT using hierarchical fast blind deconvolution

“…Our specific innovations are as follows: We propose a fast, scalable, and secure access procedure with low complexity [1], [2]. At the heart of our approach is a new fast blind deconvolution algorithm based on bilinear compressed sensing (CS) and hierarchical sparsity frameworks [3], [4], [5], [6]. The proposed algorithm has the additional advantageous feature of being inherent to low-complexity by avoiding semi-definite programming techniques.…”